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PreprintarXiv licencearXiv

Finite Time Type I Singularities of the Kähler Ricci Flow

  • Tongxin Xu
  • Zhenlei Zhang
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Abstract

We prove the Feldman--Ilmanen--Knopf conjecture for finite time Type I singularities of the Kähler--Ricci flow. More precisely, for any compact Kähler manifold Y and its blow-up π:BlpY⟶ Y, if [ω0]−Tc1(M)=π*[ωY], then any Type I parabolic blow-up limit of the Kähler Ricci flow along the exceptional divisor is the FIK shrinker Tot(𝒪ℙn−1(−1)).

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Cite

BibTeXRIS
BibTeX
@misc{xu2026finite,
  title = {{Finite Time Type I Singularities of the Kähler Ricci Flow}},
  author = {Tongxin Xu and Zhenlei Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.17458},
  eprint = {2608.17458},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.17458},
}
RIS
TY  - UNPB
TI  - Finite Time Type I Singularities of the Kähler Ricci Flow
AU  - Tongxin Xu
AU  - Zhenlei Zhang
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2608.17458
UR  - https://arxiv.org/abs/2608.17458
AB  - We prove the Feldman--Ilmanen--Knopf conjecture for finite time Type I singularities of the Kähler--Ricci flow. More precisely, for any compact Kähler manifold Y and its blow-up π:Bl_pY⟶ Y, if [ω_0]−Tc_1(M)=π^*[ω_Y], then any Type I parabolic blow-up limit of the Kähler Ricci flow along the exceptional divisor is the FIK shrinker Tot(𝒪_ℙ^n−1(−1)).
ER  -